Abstract:In recent papers tensor-product structured Nyström and Galerkin type
approximations of certain multi-dimensional integral operators have been
introduced and analysed. In the present paper we focus on the analysis of the
collocation type schemes with respect to the tensor-product basis in a high
spatial dimension d. Approximations up to an accuracy are proven to have the storage complexity with q independent of d, where N is the discrete
problem size. In particular, we apply the theory to a collocation
discretisation of the Newton potential with the kernel ,
, . Numerical illustrations are given in the
case of d=3.